Average Error: 2.0 → 1.0
Time: 5.1s
Precision: 64
\[x + \left(y - x\right) \cdot \frac{z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} = -\infty:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;x + \left(y - x\right) \cdot \frac{z}{t} \le 1.42650305201034258 \cdot 10^{295}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \end{array}\]
x + \left(y - x\right) \cdot \frac{z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} = -\infty:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

\mathbf{elif}\;x + \left(y - x\right) \cdot \frac{z}{t} \le 1.42650305201034258 \cdot 10^{295}:\\
\;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\

\mathbf{else}:\\
\;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\

\end{array}
double code(double x, double y, double z, double t) {
	return (x + ((y - x) * (z / t)));
}
↓
double code(double x, double y, double z, double t) {
	double temp;
	if (((x + ((y - x) * (z / t))) <= -inf.0)) {
		temp = (x + (((y - x) * z) / t));
	} else {
		double temp_1;
		if (((x + ((y - x) * (z / t))) <= 1.4265030520103426e+295)) {
			temp_1 = (x + ((y - x) * (z / t)));
		} else {
			temp_1 = (x + (((y - x) * z) * (1.0 / t)));
		}
		temp = temp_1;
	}
	return temp;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.0
Target2.2
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (+ x (* (- y x) (/ z t))) < -inf.0

    1. Initial program 64.0

      \[x + \left(y - x\right) \cdot \frac{z}{t}\]
    2. Using strategy rm

    3. Applied associate-*r/0.2

      \[\leadsto x + \color{blue}{\frac{\left(y - x\right) \cdot z}{t}}\]

    if -inf.0 < (+ x (* (- y x) (/ z t))) < 1.4265030520103426e+295

    1. Initial program 0.7

      \[x + \left(y - x\right) \cdot \frac{z}{t}\]

    if 1.4265030520103426e+295 < (+ x (* (- y x) (/ z t)))

    1. Initial program 27.7

      \[x + \left(y - x\right) \cdot \frac{z}{t}\]
    2. Using strategy rm

    3. Applied div-inv27.8

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(z \cdot \frac{1}{t}\right)}\]

    4. Applied associate-*r*11.4

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} = -\infty:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{elif}\;x + \left(y - x\right) \cdot \frac{z}{t} \le 1.42650305201034258 \cdot 10^{295}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot z\right) \cdot \frac{1}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.887) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

  (+ x (* (- y x) (/ z t))))